Work, Energy, and Simple Machines · Lesson 12 of 13
Lever
“Move the fulcrum, lengthen the arm, and suddenly the heavy object starts negotiating.”
• Identify the fulcrum, load, effort and arms of a lever. • Explain how a lever trades force for distance. • Apply the lever balance relation. • Calculate mechanical advantage from force or arm lengths. • Distinguish the three classes of levers by relative positions.
Place a ruler over a pencil and put a heavy stapler near the pencil on one side. A few light erasers placed farther away on the other side can lift the stapler. The small force succeeds because it acts at a greater distance from the turning point. This simple arrangement is a lever.
Activity: Let Us Investigate
Use a sturdy ruler, a pencil as a support, a stapler and identical erasers. Place the pencil closer to one end of the ruler and put the stapler on that short side. Add erasers to the far end until the stapler rises. Change the pencil position and observe how the required number of erasers changes.
A lever is a rigid bar that can rotate about a fixed point.
The fulcrum is the fixed point about which a lever rotates.
The load arm is the perpendicular distance of the load from the fulcrum.
The effort arm is the perpendicular distance of the effort from the fulcrum.
Force and Distance in a Lever
The end where a smaller effort is applied usually moves through a larger distance, while the load end moves through a smaller distance. Ignoring friction and deformation, work supplied at the effort end is transferred to the load end. A gain in force is accompanied by a loss in distance.
In balance language, the product of effort and effort arm equals the product of load and load arm.
Activity: Let Us Experiment
Suspend a long ruler from its midpoint so it can rotate freely. Attach light cups on both sides. Place one identical coin in each cup and adjust them until the beam is level. Keep one coin on the effort side, place two coins on the load side and move the heavier cup closer to the fulcrum until balance is restored. Repeat with more coins and record force and distance.
The observations show that a larger load can be balanced by placing it closer to the fulcrum, or by placing a smaller effort farther away. The force alone does not determine balance; the arm length matters equally.
Mechanical Advantage of a Lever
Increasing the effort arm while keeping the load arm fixed increases mechanical advantage. This is why a long handle can make lifting or opening easier. The smaller effort must move through a larger arc, preserving the ideal work balance.
Problem
A seesaw has seats 2 m and 1 m from its fulcrum on each side. Where should children of masses 15 kg and 30 kg sit to balance it?
- 1.The heavier child must sit closer to the fulcrum.
- 2.Place the 15 kg child at the seat 2 m from the fulcrum.
- 3.Let the 30 kg child sit at distance L on the opposite side.
- 4.Use mass × arm on one side = mass × arm on the other because g cancels.
- 5.15 × 2 = 30 × L.
- 6.L = 30 ÷ 30 = 1 m.
- 7.The 30 kg child should sit 1 m from the fulcrum.
Problem
A lever has an effort arm of 1.2 m and a load arm of 0.3 m. Find its ideal mechanical advantage and the effort needed to lift a 400 N load.
- 1.Mechanical advantage = effort arm ÷ load arm.
- 2.Mechanical advantage = 1.2 ÷ 0.3 = 4.
- 3.Use mechanical advantage = load ÷ effort.
- 4.Write 4 = 400 N ÷ effort.
- 5.Effort = 400 N ÷ 4 = 100 N.
Classes of Levers
Levers are grouped by which part lies between the other two. In a first-class lever, the fulcrum lies between effort and load. In a second-class lever, the load lies between fulcrum and effort. In a third-class lever, the effort lies between fulcrum and load.
| Class | Part in the Middle | Examples |
|---|---|---|
| Class I | Fulcrum | Scissors, crowbar, pliers, balance and seesaw |
| Class II | Load | Lemon squeezer, wheelbarrow and bottle opener |
| Class III | Effort | Tweezers, broom, hammer used in a swinging action and oar |
Levers in Everyday Tasks
A spoon used to lift a tightly fitted lid acts as a lever. The rim of the container provides a fulcrum, the hand supplies effort along the handle and the lid is the load. Scissors cut hard material more effectively near the fulcrum because the load arm is shorter there, allowing a larger force at the cutting point.
Why Perpetual Machines Do Not Work
Real machines experience friction, deformation and air resistance. Mechanical energy is continually transferred into thermal energy and sound. A machine cannot continue doing useful work forever without receiving energy from an external source. Levers and other machines rearrange force and distance; they do not create energy.
Use the appropriate distance from the fulcrum to the line of action of each force. Do not use the full bar length unless it is actually the required arm.
Quiz
Which description best matches Lever?
Which description best matches Fulcrum?
Which term matches this description: A lever is a rigid bar that can rotate about a fixed point.
Which term matches this description: The fulcrum is the fixed point about which a lever rotates.
Which statement is a key takeaway from this lesson?
Practice Problems
- A 200 N load acts 0.2 m from a fulcrum. Find the effort needed 0.8 m from the fulcrum.
- Classify a seesaw, wheelbarrow and tweezers by lever class.
- Explain why cutting near the pivot of scissors helps with a hard object.
- A lever has mechanical advantage 5 and lifts a 750 N load. Find the ideal effort.
Key Takeaways
• A lever rotates about a fulcrum. • Balance depends on force multiplied by arm length. • A longer effort arm can reduce the required effort. • Mechanical advantage equals effort arm divided by load arm. • Lever classes depend on the relative positions of fulcrum, load and effort.